Testing the effect of deviance on similarity-based structure and certainty.
Hypothesis: We predict that as a new agent’s deviance from the group stereotype increases there will be a transition from group updating to subgroup formation to subtype formation. This will be reflected in participants’ similarity-rating derived dendrograms.
Method changes: 6 agents, 12 issues
| 0 (N=62) |
0.25 (N=50) |
0.5 (N=55) |
0.75 (N=49) |
1 (N=57) |
Overall (N=273) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 37.4 (12.2) | 37.8 (14.6) | 34.2 (10.3) | 37.2 (12.5) | 37.8 (11.5) | 36.9 (12.2) |
| Median [Min, Max] | 36.5 [20.0, 64.0] | 34.0 [19.0, 75.0] | 34.0 [19.0, 69.0] | 34.0 [18.0, 65.0] | 35.0 [20.0, 64.0] | 35.0 [18.0, 75.0] |
| race | ||||||
| Asian | 6 (9.7%) | 1 (2.0%) | 6 (10.9%) | 7 (14.3%) | 5 (8.8%) | 25 (9.2%) |
| Black or African-American | 5 (8.1%) | 2 (4.0%) | 6 (10.9%) | 3 (6.1%) | 8 (14.0%) | 24 (8.8%) |
| Hispanic/Latinx | 10 (16.1%) | 2 (4.0%) | 4 (7.3%) | 3 (6.1%) | 4 (7.0%) | 23 (8.4%) |
| White | 41 (66.1%) | 44 (88.0%) | 39 (70.9%) | 35 (71.4%) | 39 (68.4%) | 198 (72.5%) |
| Native Hawaiian or Other Pacific Islander | 0 (0%) | 1 (2.0%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (0.4%) |
| American Indian or Alaska Native | 0 (0%) | 0 (0%) | 0 (0%) | 1 (2.0%) | 0 (0%) | 1 (0.4%) |
| Other | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (1.8%) | 1 (0.4%) |
| gender | ||||||
| Man | 23 (37.1%) | 23 (46.0%) | 32 (58.2%) | 25 (51.0%) | 27 (47.4%) | 130 (47.6%) |
| Non-binary | 1 (1.6%) | 1 (2.0%) | 1 (1.8%) | 0 (0%) | 2 (3.5%) | 5 (1.8%) |
| Woman | 38 (61.3%) | 26 (52.0%) | 21 (38.2%) | 24 (49.0%) | 25 (43.9%) | 134 (49.1%) |
| Prefer not to answer | 0 (0%) | 0 (0%) | 1 (1.8%) | 0 (0%) | 2 (3.5%) | 3 (1.1%) |
| Another gender not listed here | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (1.8%) | 1 (0.4%) |
| 0 (N=3) |
0.25 (N=7) |
0.5 (N=5) |
0.75 (N=7) |
1 (N=4) |
Overall (N=26) |
|
|---|---|---|---|---|---|---|
| age | ||||||
| Mean (SD) | 29.7 (12.4) | 39.6 (9.07) | 26.4 (5.68) | 38.1 (20.2) | 24.3 (4.92) | 33.2 (13.4) |
| Median [Min, Max] | 23.0 [22.0, 44.0] | 38.0 [30.0, 57.0] | 24.0 [22.0, 36.0] | 27.0 [19.0, 68.0] | 24.0 [20.0, 29.0] | 28.5 [19.0, 68.0] |
| race | ||||||
| White | 3 (100%) | 4 (57.1%) | 3 (60.0%) | 4 (57.1%) | 2 (50.0%) | 16 (61.5%) |
| Asian | 0 (0%) | 1 (14.3%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (3.8%) |
| Black or African-American | 0 (0%) | 2 (28.6%) | 1 (20.0%) | 3 (42.9%) | 1 (25.0%) | 7 (26.9%) |
| Hispanic/Latinx | 0 (0%) | 0 (0%) | 1 (20.0%) | 0 (0%) | 1 (25.0%) | 2 (7.7%) |
| gender | ||||||
| Man | 1 (33.3%) | 5 (71.4%) | 2 (40.0%) | 5 (71.4%) | 2 (50.0%) | 15 (57.7%) |
| Non-binary | 1 (33.3%) | 0 (0%) | 0 (0%) | 0 (0%) | 0 (0%) | 1 (3.8%) |
| Woman | 1 (33.3%) | 2 (28.6%) | 3 (60.0%) | 2 (28.6%) | 2 (50.0%) | 10 (38.5%) |
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: corrresp
Chisq Df Pr(>Chisq)
opinion_round 195.4479 1 < 2.2e-16 ***
Deviant_threshold 33.2358 4 1.069e-06 ***
opinion_round:Deviant_threshold 7.0631 4 0.1326
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 1 opinion_round.trend SE df asymp.LCL asymp.UCL z.ratio p.value
overall 0.113 0.00807 Inf 0.0976 0.129 14.052 <.0001
Results are averaged over the levels of: Deviant_threshold
Confidence level used: 0.95 $emmeans
Deviant_threshold emmean SE df asymp.LCL asymp.UCL z.ratio p.value
0 1.533 0.100 Inf 1.336 1.73 15.293 <.0001
0.25 1.003 0.109 Inf 0.789 1.22 9.218 <.0001
0.5 0.850 0.103 Inf 0.648 1.05 8.273 <.0001
0.75 0.863 0.109 Inf 0.649 1.08 7.905 <.0001
1 0.946 0.101 Inf 0.748 1.15 9.332 <.0001
Results are given on the logit (not the response) scale.
Confidence level used: 0.95
$contrasts
contrast estimate SE df asymp.LCL
Deviant_threshold0 - Deviant_threshold0.25 0.5301 0.147 Inf 0.129
Deviant_threshold0 - Deviant_threshold0.5 0.6831 0.143 Inf 0.294
Deviant_threshold0 - Deviant_threshold0.75 0.6698 0.147 Inf 0.268
Deviant_threshold0 - Deviant_threshold1 0.5863 0.142 Inf 0.200
Deviant_threshold0.25 - Deviant_threshold0.5 0.1530 0.149 Inf -0.253
Deviant_threshold0.25 - Deviant_threshold0.75 0.1397 0.153 Inf -0.278
Deviant_threshold0.25 - Deviant_threshold1 0.0562 0.148 Inf -0.347
Deviant_threshold0.5 - Deviant_threshold0.75 -0.0133 0.149 Inf -0.420
Deviant_threshold0.5 - Deviant_threshold1 -0.0968 0.143 Inf -0.488
Deviant_threshold0.75 - Deviant_threshold1 -0.0835 0.148 Inf -0.487
asymp.UCL z.ratio p.value
0.931 3.609 0.0028
1.072 4.793 <.0001
1.071 4.550 0.0001
0.972 4.143 0.0003
0.558 1.029 0.8420
0.558 0.912 0.8925
0.459 0.380 0.9956
0.393 -0.089 1.0000
0.294 -0.675 0.9619
0.320 -0.564 0.9802
Results are given on the log odds ratio (not the response) scale.
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
targetpair 632 632 1 273 2.9882 0.08501 .
Deviant_threshold 57300 57300 1 273 271.0453 < 2e-16 ***
targetpair:Deviant_threshold 42838 42838 1 273 202.6359 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emtrends
targetpair Deviant_threshold.trend SE df lower.CL upper.CL t.ratio p.value
DN -63.68 2.97 273 -69.5 -57.829 -21.415 <.0001
NN -5.91 2.89 273 -11.6 -0.234 -2.050 0.0414
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio p.value
DN - NN -57.8 4.06 273 -65.8 -49.8 -14.235 <.0001
Degrees-of-freedom method: satterthwaite
Confidence level used: 0.95 Analysis of Variance Table
Response: k
Df Sum Sq Mean Sq F value Pr(>F)
Deviant_threshold 4 28.224 7.0559 14.391 1.174e-10 ***
Residuals 268 131.405 0.4903
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
Deviant_threshold emmean SE df lower.CL upper.CL t.ratio p.value
0 1.68 0.0889 268 1.50 1.85 18.869 <.0001
0.25 1.65 0.0990 268 1.45 1.84 16.616 <.0001
0.5 2.11 0.0944 268 1.92 2.29 22.303 <.0001
0.75 2.27 0.1000 268 2.07 2.46 22.660 <.0001
1 2.45 0.0927 268 2.27 2.63 26.424 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL
Deviant_threshold0 - Deviant_threshold0.25 0.0325 0.133 268 -0.333
Deviant_threshold0 - Deviant_threshold0.5 -0.4278 0.130 268 -0.784
Deviant_threshold0 - Deviant_threshold0.75 -0.5888 0.134 268 -0.956
Deviant_threshold0 - Deviant_threshold1 -0.7728 0.128 268 -1.126
Deviant_threshold0.25 - Deviant_threshold0.5 -0.4603 0.137 268 -0.836
Deviant_threshold0.25 - Deviant_threshold0.75 -0.6213 0.141 268 -1.008
Deviant_threshold0.25 - Deviant_threshold1 -0.8053 0.136 268 -1.178
Deviant_threshold0.5 - Deviant_threshold0.75 -0.1610 0.138 268 -0.539
Deviant_threshold0.5 - Deviant_threshold1 -0.3450 0.132 268 -0.708
Deviant_threshold0.75 - Deviant_threshold1 -0.1840 0.136 268 -0.559
upper.CL t.ratio p.value
0.3981 0.244 0.9992
-0.0716 -3.298 0.0097
-0.2212 -4.399 0.0002
-0.4199 -6.014 <.0001
-0.0845 -3.364 0.0078
-0.2347 -4.414 0.0001
-0.4327 -5.935 <.0001
0.2168 -1.170 0.7682
0.0185 -2.606 0.0720
0.1907 -1.349 0.6610
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates Deviant_threshold emmean SE df null t.ratio p.value
0 1.68 0.0889 268 2 -3.621 0.0002
0.25 1.65 0.0990 268 2 -3.580 0.0002
0.5 2.11 0.0944 268 2 1.120 0.8682
0.75 2.27 0.1000 268 2 2.667 0.9959
1 2.45 0.0927 268 2 4.860 1.0000
P values are left-tailed # A tibble: 2 × 13
model term estimate std.error statistic p.value conf.low
<chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 below_.5 Deviant_threshold -16.3 10.0 -1.63 0.106 -36.1
2 above_.5 Deviant_threshold -14.6 10.1 -1.44 0.151 -34.6
conf.high r.squared adj.r.squared df df.residual nobs
<dbl> <dbl> <dbl> <dbl> <int> <int>
1 3.49 0.0158 0.00981 1 165 167
2 5.39 0.0129 0.00670 1 159 161Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 7877 1969.31 2.734 0.02942 *
Residuals 268 193044 720.31
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1$emmeans
deviance emmean SE df lower.CL upper.CL t.ratio p.value
0 61.1 3.41 268 54.4 67.8 17.915 <.0001
0.25 53.2 3.80 268 45.8 60.7 14.027 <.0001
0.5 53.1 3.62 268 45.9 60.2 14.660 <.0001
0.75 48.7 3.83 268 41.2 56.3 12.711 <.0001
1 45.8 3.55 268 38.8 52.8 12.871 <.0001
Confidence level used: 0.95
$contrasts
contrast estimate SE df lower.CL upper.CL t.ratio
deviance0 - deviance0.25 7.825 5.10 268 -6.19 21.8 1.534
deviance0 - deviance0.5 8.010 4.97 268 -5.64 21.7 1.611
deviance0 - deviance0.75 12.330 5.13 268 -1.76 26.4 2.403
deviance0 - deviance1 15.310 4.92 268 1.78 28.8 3.109
deviance0.25 - deviance0.5 0.185 5.24 268 -14.22 14.6 0.035
deviance0.25 - deviance0.75 4.505 5.40 268 -10.31 19.3 0.835
deviance0.25 - deviance1 7.486 5.20 268 -6.80 21.8 1.439
deviance0.5 - deviance0.75 4.320 5.27 268 -10.16 18.8 0.819
deviance0.5 - deviance1 7.300 5.07 268 -6.63 21.2 1.439
deviance0.75 - deviance1 2.980 5.23 268 -11.38 17.3 0.570
p.value
0.5414
0.4915
0.1175
0.0176
1.0000
0.9195
0.6027
0.9245
0.6030
0.9793
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 5 estimates
P value adjustment: tukey method for comparing a family of 5 estimates | 0 (N=62) |
0.25 (N=50) |
0.5 (N=55) |
0.75 (N=49) |
1 (N=57) |
Overall (N=273) |
|
|---|---|---|---|---|---|---|
| pred_maj | ||||||
| Yes | 50 (80.6%) | 40 (80.0%) | 41 (74.5%) | 41 (83.7%) | 41 (71.9%) | 213 (78.0%) |
| No | 12 (19.4%) | 10 (20.0%) | 14 (25.5%) | 8 (16.3%) | 16 (28.1%) | 60 (22.0%) |
# A tibble: 4 × 14
# Groups: pred_maj [2]
pred_maj id term estimate std.error statistic p.value
<lgl> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 FALSE below_.5 Deviant_threshold -3.97 21.4 -0.186 0.854
2 FALSE above_.5 Deviant_threshold -8.20 20.2 -0.406 0.687
3 TRUE below_.5 Deviant_threshold -18.7 11.3 -1.64 0.102
4 TRUE above_.5 Deviant_threshold -16.2 11.6 -1.40 0.165
conf.low conf.high r.squared adj.r.squared df df.residual nobs
<dbl> <dbl> <dbl> <dbl> <dbl> <int> <int>
1 -47.4 39.4 0.00101 -0.0284 1 34 36
2 -49.1 32.7 0.00457 -0.0231 1 36 38
3 -41.1 3.79 0.0205 0.0129 1 129 131
4 -39.3 6.80 0.0158 0.00770 1 121 123Analysis of Variance Table
Response: confidence
Df Sum Sq Mean Sq F value Pr(>F)
deviance 4 7877 1969.3 2.7662 0.02795 *
pred_maj 1 3435 3435.3 4.8253 0.02892 *
deviance:pred_maj 4 2372 593.1 0.8330 0.50518
Residuals 263 187236 711.9
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1| 0 (N=273) |
1 (N=273) |
2 (N=273) |
3 (N=273) |
4 (N=273) |
5 (N=273) |
6 (N=273) |
7 (N=273) |
8 (N=273) |
9 (N=273) |
10 (N=273) |
11 (N=273) |
Overall (N=3276) |
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| trialnum | |||||||||||||
| 0 | 46 (16.8%) | 49 (17.9%) | 41 (15.0%) | 44 (16.1%) | 39 (14.3%) | 48 (17.6%) | 37 (13.6%) | 48 (17.6%) | 39 (14.3%) | 47 (17.2%) | 49 (17.9%) | 63 (23.1%) | 550 (16.8%) |
| 1 | 49 (17.9%) | 50 (18.3%) | 43 (15.8%) | 46 (16.8%) | 42 (15.4%) | 46 (16.8%) | 48 (17.6%) | 49 (17.9%) | 46 (16.8%) | 44 (16.1%) | 52 (19.0%) | 42 (15.4%) | 557 (17.0%) |
| 2 | 45 (16.5%) | 41 (15.0%) | 43 (15.8%) | 39 (14.3%) | 55 (20.1%) | 44 (16.1%) | 36 (13.2%) | 54 (19.8%) | 50 (18.3%) | 53 (19.4%) | 56 (20.5%) | 39 (14.3%) | 555 (16.9%) |
| 3 | 43 (15.8%) | 43 (15.8%) | 43 (15.8%) | 46 (16.8%) | 43 (15.8%) | 44 (16.1%) | 58 (21.2%) | 41 (15.0%) | 36 (13.2%) | 41 (15.0%) | 39 (14.3%) | 41 (15.0%) | 518 (15.8%) |
| 4 | 41 (15.0%) | 41 (15.0%) | 47 (17.2%) | 50 (18.3%) | 57 (20.9%) | 51 (18.7%) | 45 (16.5%) | 42 (15.4%) | 57 (20.9%) | 44 (16.1%) | 35 (12.8%) | 45 (16.5%) | 555 (16.9%) |
| 5 | 49 (17.9%) | 49 (17.9%) | 56 (20.5%) | 48 (17.6%) | 37 (13.6%) | 40 (14.7%) | 49 (17.9%) | 39 (14.3%) | 45 (16.5%) | 44 (16.1%) | 42 (15.4%) | 43 (15.8%) | 541 (16.5%) |